We consider two real-world binary-classification tasks: predicting
the reactivity of a chemical and predicting mortality in the intensive care unit (ICU).
For both tasks we use Bayesian logistic regression.
Bayesian logistic regression is a conditional prediction model with prior \(p(\mathbf {w})~=~\mathcal {N}(0,1)\)  and conditional likelihood \(p(\mathbf {y}|\mathbf {X}) = \text{Bernoulli}(p = \text{sigmoid}(\mathbf {X}^\top \mathbf {w}))\) .
This model is commonly used as an example of a simple model which does not have a closed-form posterior [1]}.
We set the base family to be the Laplace distributions following [2]}.
